Solve for $x$ and $y$ using elimination. ${-5x-3y = -35}$ ${-2x+5y = 48}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $2$ and the bottom equation by $-5$ ${-10x-6y = -70}$ $10x-25y = -240$ Add the top and bottom equations together. $-31y = -310$ $\dfrac{-31y}{{-31}} = \dfrac{-310}{{-31}}$ ${y = 10}$ Now that you know ${y = 10}$ , plug it back into $\thinspace {-5x-3y = -35}\thinspace$ to find $x$ ${-5x - 3}{(10)}{= -35}$ $-5x-30 = -35$ $-5x-30{+30} = -35{+30}$ $-5x = -5$ $\dfrac{-5x}{{-5}} = \dfrac{-5}{{-5}}$ ${x = 1}$ You can also plug ${y = 10}$ into $\thinspace {-2x+5y = 48}\thinspace$ and get the same answer for $x$ : ${-2x + 5}{(10)}{= 48}$ ${x = 1}$